Ph.D. (2010) Massachusetts Institute of Technology
Algebraic and geometric combinatorics
I am interested in the interplay between algebra, geometry and combinatorics. Most recently I have been studying flow (and root) polytopes and their connections to (1) Kostant partition functions (as established by Postnikov and Stanley and Baldoni and Vergne in the early 2000s), (2) Grothendieck polynomials (appearing in my work with Escobar) and (3) the space of diagonal harmonics (appearing in my work with Morales and Rhoades).
The polytope of Tesler matrices (with A. H. Morales and B. Rhoades), Selecta Mathematica, to appear. http://arxiv.org/abs/1409.8566
Toric matrix Schubert varieties and their polytopes (with L. Escobar), Proceedings of the American Mathematical Society, to appear. http://arxiv.org/abs/1508.03445
Subword complexes via triangulations of root polytopes (with L. Escobar), preprint. http://arxiv.org/abs/1502.03997
Product formulas for volumes of flow polytopes, Proceedings of the American Mathematical Society 143 no. 3, (2015), 937-954.
Flow polytopes of signed graphs and the Kostant partition function (with A. H. Morales), International Mathematical Research Notices no. 3, (2015), 830-871.
Root polytopes, triangulations, and the subdivision algebra, II, Transactions of the American Mathematical Society 363 no. 11, (2011), 6111-6141.
Root polytopes, triangulations, and the subdivision algebra, I, Transactions of the American Mathematical Society 363 no 8, (2011), 4359-4382.